A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation
Modulation instability (MI) is a pervasive phenomenon in nonlinear science. It is inevitable for simulating rogue wave or breather solutions of the focusing nonlinear Schrödinger equation (NLSE) and other application problems with MI involved. Due to MI, the small perturbation on the boundary can lead to large and non-negligible errors for the simulation of initial-boundary problems. To deal with this challenging problem, the authors propose a method to modify the boundary problem through a deep learning algorithm so that the long time simulation for the rogue wave or breather solutions to the NLSE can be performed with a superior numerical errors. This method paves a way to simulate other physical problems with MI.
scientific article; zbMATH DE number 7370464
scientific article